共查询到20条相似文献，搜索用时 15 毫秒
1.
Laura Stumpf 《Celestial Mechanics and Dynamical Astronomy》1999,74(2):95-109
The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of . 相似文献
2.
In this paper, an efficient iterative method of arbitrary integer order of convergence ≥ 2 has been established for solving
the hyperbolic form of Kepler’s equation. The method is of a dynamic nature in the sense that, moving from one iterative scheme
to the subsequent one, only additional instruction is needed. Most importantly, the method does not need any prior knowledge
of the initial guess. A property which avoids the critical situations between divergent and very slow convergent solutions
that may exist in other numerical methods which depend on initial guess. Computational Package for digital implementation
of the method is given and is applied to many case studies. 相似文献
3.
In the present paper, an efficient iterative method of arbitrary integer order of convergent ≥2 based on the homotopy continuation techniques for the solution of the initial value problem of space dynamics using the universal Y functions is presented. The method is of dynamic nature in the sense that, ongoing from one iterative scheme to the subsequent one, only additional instruction is needed. Most importantly, the method does not need any prior knowledge of the initial guess. This is a property which avoids the critical situations between divergent to very slow convergent solutions that may exist in other numerical methods which depend on initial guesses. A computational package for digital implementation of the method is given, together with numerical applications for elliptic, hyperbolic, and parabolic orbits. The accuracy of the results for all orbits is O(10–16). (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
In this paper, we consider a statistical method for distance determination of stellar groups. The method depends on the assumption
that the members of the group scatter around a mean absolute magnitude in Gaussian distribution. The mean apparent magnitude
of the members is then expressed by frequency function, so as to correct for observational incompleteness at the faint end.
The problem reduces to the solution of a highly transcendental equation for a given magnitude parameter α. For the computational developments of the problem, continued fraction by the Top-Down algorithm was developed and applied
for the evaluation of the error function erf(z). The distance equation Λ(y) = 0 was solved by an iterative method of second order of convergence using homotopy continuation technique. This technique
does not need any prior knowledge of the initial guess, a property which avoids the critical situations between divergent
and very slow convergent solutions, that may exist in the applications of other iterative methods depending on initial guess. 相似文献
5.
Edward W. Ng 《Celestial Mechanics and Dynamical Astronomy》1979,20(3):243-249
An efficient algorithm is presented for the solution of Kepler's equationf(E)=E–M–e sinE=0, wheree is the eccentricity,M the mean anomaly andE the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics inM, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20 000 pairs of values ofe andM show that for single precision (10–8) 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision (10–18) one additional iteration is required. Single- and double-precision FORTRAN subroutines are available from the author. 相似文献
6.
The numerical method for obtaining the luminosity-dependent evolution function of radio sources is presented and applied to the flat spectrum radio sources selected at 5 GHz.The method constructed on the basis of the iterative one given by Robertson, which requires assuming a specific type of the searched function enables one to obtain the evolution function of sources with radio flux densityS
5.01 mJy.The influence of the shape of the local RLF, of the luminosity distributionN(P) and of the spectral index function on the resulting evolution function is investigated. The results presented show that the luminosity dependence of the evolution function of flat-spectrum radio sources is significant and should not be neglected. The obtained evolution function, which allows one to reproduce the source counts curve, the redshift distribution, and the spectral index distribution, may exhibit the redshift cut-off at z03. 相似文献
7.
K. N. Yu 《Astrophysics and Space Science》1987,137(1):93-99
We adopt the iterative least-squares method of Schmee and Hahn (1979) and extend it to the multiple regression case to investigate the dependence of the X-ray luminositíesL
x
of quasars on their optical liminositiesL
0 and redshiftsz. The method has several advantages, one of which is that we do not need the strong assumption that the values of the optical-X-ray index 0x
of the detected and nondetected quasars should fall into the same range. We have found that correlations of 0x
and log(1+z) or the look back time (z) are shown, but these are not firmly established due to the uncertainty present in the regression parameter. On the other hand, it is impossible for 0x
to be independent ofL
0. We have also shown thatL
x
is less than proportional toL
0. 相似文献
8.
A new numerical method is proposed for solving the problems connected with the evolution of spherical clusters. The method is based upon the solution of the algebraic equations describing the motions of spherical shells.The stage of the collapse of a typical cluster is considered. The initial configuration is taken as a system with a uniform density distribution and with velocities much less than the virial ones. The model close to a stationary one has been obtained. The mass of the stationary cluster comprises about 60% of the initial one. The density distribution of the outer part of the cluster approximately corresponds to a profile of R
–3.3. 相似文献
9.
We consider that single loop flares can be caused by the rotation of loop footpoints. Choosing a typical geometry for this case we find from MHD equations self-consistent expressions and a set equations governing behaviour of all physical quantities. Numerical simulations have revealed that under the determined conditions for the initial azimuthal velocity and current the pinch instability takes place. The most important parameters of the problem are the plasma and the ratio of the initial values of longitudinal and poloidal components of the magnetic field-B
1. Thus, calculations show that the critical pinch time increases with the increase ofB
1 and decreases with the increase of plasma . So the most effective flares are probable for the most high loops with strong currents. ForB
1=10 and =0.01 the critical pinch time is 2.5 s. The critical twist angle for magnetic field depends on the initial one. For low intial twist which corresponds to bigB
1 the critical one is more less. For exampleB
1=30 gives 1.8 (when ratio of loop length and radius is 10). Geometrical analysis shows that the present model can explain (for high photospheric rotation) single loop flares taking place on different parts of the loop as on the top of it as closer to one of the footpoints. It depends on the relative rotation momentum of loop footpoints. Subject headings: MHD-Sun:flares. 相似文献
10.
O. Demircan 《Astrophysics and Space Science》1977,47(2):459-488
Kopal's new iterative method for analysing partially eclipsing binary light curves in the frequency domain has been put into a form suitable for applications, and explicit forms for basic expressions developed. To facilitate the computations in practice, the required newS
m
-functions, which are expressed in terms ofJ
,
0
-integrals, have been extensively tabulated by making use of hypergeometric series. The automated method has been tested successfully on the light curves of Persei (Algol). Short information on the system and the revised sets of elements including a new determination of the limb-darkening coefficient in the ultraviolet have been presented. 相似文献
11.
S. I. Grachev 《Astrophysics》2001,44(4):505-517
A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity of t, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + t, and so forth. The method enables one to analyze nonsteady tradiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples. 相似文献
12.
H. Ma G. Baù D. Bracali Cioci G. F. Gronchi 《Celestial Mechanics and Dynamical Astronomy》2018,130(10):70
We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in Gronchi et al. (Mon Not R Astron Soc 451(2):1883–1891, 2015b), which uses a pure Keplerian dynamical model. Since the effect of the Earth oblateness is strong at low altitudes, its inclusion in the model can sensibly improve the initial orbit, giving a better starting guess for differential corrections and increasing the chances to obtain their convergence. The input set consists of two tracks of radar observations, each one composed of at least four observations taken during the same pass of the satellite. A single observation gives the topocentric position of the satellite, where the range is very accurate, while the line-of-sight direction is poorly determined. From these data, we can compute by a polynomial fit the values of the range and range rate at the mean epochs of the two tracks. In order to obtain a preliminary orbit, we wish to compute the angular velocity, which is the rate of change of the line of sight. In the same spirit of Gronchi et al. (Mon Not R Astron Soc 451(2):1883–1891, 2015b), we also wish to correct the values of the angular measurements, so that they fit the selected dynamical model if the same holds for the radial distance and velocity. The selected model is a perturbed Keplerian dynamics, where the only perturbation included is the secular effect of the \(J_2\) term of the geopotential. 相似文献
13.
I. A. Robin 《Celestial Mechanics and Dynamical Astronomy》1981,23(1):97-106
We show that the procedure employed in the circular restricted problem, of tracing families of three-dimensional periodic orbits from vertical self-resonant orbits belonging to plane families, can also be applied in the elliptic problem. A method of determining series of vertical bifurcation orbits in the planar elliptic restricted problem is described, and one such series consisting of vertical-critical orbits (a
v=+1) is given for the entire range (0,1/2) of the mass parameter . The initial segments of the families of three-dimensional orbits which bifurcate from two of the orbits belonging to this series are also given. 相似文献
14.
We compare the results of two distinct methods for deriving photospheric vector magnetic fields from the Zeeman effect as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA.). One method ignores magneto-optical effects but allows for an absolute determination of B from the integral properties of the Stokes profiles, under the assumption of weak field strength. The other method is an iterative least-squares fitting technique developed by Lites and Skumanich which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. We find empirically that for sunspot fields above 1500 gauss the two methods agree in derived azimuthal and inclination angles to within ± 20 degs., Furthermore, for such fields, the estimate of the line of sight field and the transverse field derived using the two methods agree to within ± 500 gauss. In weak field strength regions the integral method can be used with little error and computational load in the estimation of the line of sight field, the transverse field and the inclination angle but the disagreement in derived azimuthal angle is considerable ( ± 90 degs.). 相似文献
15.
The fragmentation of a molecular cloud is modelled as a random process by the Monte Carlo method. The probability of the fragmentation is a function of the cloud initial mass and decreases rapidly for mass lower than critical mass, which is a defined parameter. The modelled IMF is compared with the mean mass function in open clusters assumed here as the observed IMF. The best fit was found for initial mass 3×103
M
s
and for the critical mass range 0.4 to 0.6M
s
. It also implies the star formation efficiency to be about 0.3.Paper presented at a Workshop on The Role of Dust in Dense Regions of Interstellar Matter, held at Georgenthal, G.D.R., in March 1986. 相似文献
16.
A. A. Van Ballegooijen 《Solar physics》1984,91(2):195-217
From a high-resolution spectrum of a sunspot umbra (1.1 < < 2.3 m) we derive models of the temperature stratification in the deep layers of the umbra. The observed spectrum is corrected for straylight using the Hi Paschen line at gl = 1.282 m. A method is described for the iterative fitting of empirical temperature models to spectral information, and the method is applied to the present data. We find that the observed profiles of 3 high-excitation lines of Sii and the observed continuum contrast between umbra and photosphere cannot be reproduced with a single one-component model of the umbral atmosphere: the Si i lines require a model that is 460 K hotter at gt
0.5 = 3 than the continuum model. This indicates that hot and cool components coexist within the umbra. A temperature model derived from the relative intensity in the wings of 3 low-excitation lines of Mgi, Ali, and Sii is not significantly different from the continuum model.Based on observations obtained at Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under contract with the National Science Foundation. 相似文献
17.
A model of two-current-loop collisions is presented to explain the impulsive nature of solar flares. From MHD equations considering the gravity and resistivity effects we find self-consistent expressions and a set of equations governing the behavior of all physical quantities just after magnetic reconnection has taken place. Numerical simulations have revealed that the most important parameters of the problem are the plasma and the ratio of initial values of pressure gradient in the longitudinal and radial directions. Thus, the low plasma case during aY-type interaction (initial longitudinal pressure gradient is comparable with initial radial pressure gradient) shows a rapid pinch and simultaneous enhancement of all physical quantities, including the electric field components, which are important for high-energy particle acceleration. However, an increase of the plasma causes a weakening of the pinch effect and a decrease of extreme values of all physical quantities. On the other hand, for anX-type collision (initial longitudinal pressure gradient is much greater than initial radial pressure gradient), which is able to provide a jet, the increase of the plasma causes a high velocity jet. As for aI-type collision (initial longitudinal pressure gradient is much less than initial radial pressure gradient) it shows neither jet production nor very strong enhancement of physical quantities. We also consider direct and oblique collisions, taking into account both cases of partial and complete reconnection. 相似文献
18.
In this paper the gravitational collapse of cosmic gas clouds and formation of star clusters has been considered. Hoyle's view of successive fragmentation has been taken as the basic mechanim in the present work. The initial masses of protostars have been estimated as the function of their distances from the centre of the cluster and the intensity of the magnetic field of the medium. It has been shown that the fragmentation process is greatly inhibited by the presence of a strong magnetic field. A model has been constructed showing how a protostar grows in mass by accretion from the surrounding medium, on the basis of the assumption that as the star moves at random in the cluster it picks up a fraction of the material through which it passes. It has been estimated that a protostar of initial mass of about 0.1M
grows to one of 1.0M
in a time period which ranges from a few multiples of 105 to a few multiples of 107 yr, depending on the parameters involved in the accretion process. The number of stars per unit mass range has also been estimated; it is found to be proportional tom
–3.3,m being the mass of the star. 相似文献
19.
Jean Meffroy 《Earth, Moon, and Planets》1980,23(1):73-97
Using a method previously applied to the treatment of the Mathieu differential equation, we solve the Hill's differential equation of lunar theory through the way of operational calculus, which avoids the cumbersome infinite determinants of the classical procedure. The one-sided Laplace transformation changes it into a difference equation with an infinite number of terms and variable coefficients. When its first member is divided by a suitable factor, this difference equation is the image of an integral equation of the Volterra type which is equivalent to the initial Hill's differential equation. Solution of this Volterra integral equation is unique and it is the general solution of the Hill's differential equation. This solution is a series in the powers of a small dimensionless parameter
2 which appears as a factor in the second member of the Hill's differential equation. We reduce it to the sum of its terms of degree 12 with respect to which is the precision usually required in a lunar theory and we write down effectively the coefficients of the terms in
2, (
2)2 and the coefficient of the term in (
2)3 which depends upon the initial valuey(0) of the Hill's differential equation. 相似文献
20.
This paper presents the development and testing of a new iterative reconstruction algorithm for astronomy. We propose a maximuma posteriori method of image reconstruction in the Bayesian statistical framework for the Poisson noise case. The method uses the entropy with an adjustable sharpness parameter to define the prior probability and the likelihood with data increment parameters to define the conditional probability. The method allows us to obtain reconstructions with neither the problem of the grey reconstructions associated with the pure Bayesian reconstructions nor the problem of image deterioration, typical of the maximum likelihood method. Our iterative algorithm is fast, stable, maintains positivity, and converges to feasible images.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain. 相似文献